A partial solution for Feynman's problem – a new derivation of the Weyl equation.
A polynomial invariant of rational homology 3-spheres.
A possible approach to inclusion of space and time in frame fields of quantum representations of real and complex numbers.
A problem related to the Hall effect in a semiconductor with an electrode of an arbitrary shape.
À propos du calcul différentiel sur les groupes quantiques
A Pseudo-Algebra of Observables for the Dirac Equation.
A -analogue of the centralizer construction and skew representations of the quantum affine algebra.
A quantization procedure of fields based on geometric Langlands correspondence.
A quantum field theoretical representation of Euler-Zagier sums.
A quantum particle in a quadrupole radio-frequency trap
A recurrence relation approach to higher order quantum superintegrability.
A relation between the multiplicity of the second eigenvalue of a graph Laplacian, Courant's nodal line theorem and the substantial dimension of tight polyhedral surfaces.
A remark on natural quantum Lagrangians and natural generalized Schrödinger operators in Galilei quantum mechanics
A remark on the comparison of Mackey and Segal models
A remark on the paper “Une martingale d'opérateurs bornés, non représentable en intégrale stochastique”, by J.L. Journé and P.A. Meyer
A representation independent propagator I : compact Lie groups
A representation independent propagator. II : Lie groups with square integrable representations
A representation of orthomodular lattices
A representation of the coalgebra of derivations for smooth spaces
Let be a field. The generalized Leibniz rule for higher derivations suggests the definition of a coalgebra for any positive integer . This is spanned over by , and has comultiplication and counit defined by and (Kronecker’s delta) for any . This note presents a representation of the coalgebra by using smooth spaces and a procedure of microlocalization. The author gives an interpretation of this result following the principles of the quantum theory of geometric spaces.
A Reproducing Kernel and Toeplitz Operators in the Quantum Plane
We define and analyze Toeplitz operators whose symbols are the elements of the complex quantum plane, a non-commutative, infinite dimensional algebra. In particular, the symbols do not come from an algebra of functions. The process of forming operators from non-commuting symbols can be considered as a second quantization. To do this we construct a reproducing kernel associated with the quantum plane. We also discuss the commutation relations of creation and annihilation operators which are defined...